Preheat oven to 425 degrees with a pizza stone placed on the lowest rack.

Sprinkle enough cornmeal to lightly cover a pizza peel. Stretch and roll out dough to a rough 12" to 13" circle and transfer to the cornmeal-dusted peel. Drizzle crust with 1 tablespoon oil and rub all over to coat. Sprinkle with dried basil. Slide crust onto the stone and bake until the bottom just begins to brown, about 5 to 7 minutes. Carefully remove from the oven and place the crust onto a wire rack.

Scatter mozzarella in a 4" circle on the center of the dough. Using about 3 ounces (3/4 cup) of the cheddar, scatter a 3" ring around the mozzarella. Evenly spoon pizza sauce over the Cheddar ring. Scatter remaining Cheddar from around the edge of the pizza sauce ring to the edge of the crust.

Slide pizza back onto the stone and bake until the cheese has melted, about 8 to 12 minutes. Remove from the oven and place pizza on a wire rack to cool slightly before serving.